The radius of the smaller circle is approximately 18.3 cm, and the radius of the larger circle is approximately 28.3 cm.
To find the radius of the two circles, let's follow these steps:
1. Let's assume the radius of the smaller circle is "r" cm. Since the radius of the larger circle is 10 cm greater, its radius will be "r + 10" cm.
2. The formula to find the circumference of a circle is given by C = 2πr, where C is the circumference and π is a constant value approximately equal to 3.14.
3. The total length of the wire, 136 cm, is equal to the sum of the circumferences of the two circles. We can write this as an equation:
2πr + 2π(r + 10) = 136
4. Simplify the equation:
2πr + 2πr + 20π = 136
5. Combine like terms:
4πr + 20π = 136
6. Divide both sides of the equation by 4π to isolate the variable "r":
r + 5π = 34
7. Subtract 5π from both sides:
r = 34 - 5π
8. Since π is an irrational number, we can use an approximation of π as 3.14 to find a numerical value for "r":
r ≈ 34 - 5(3.14)
r ≈ 34 - 15.7
r ≈ 18.3
9. So, the radius of the smaller circle is approximately 18.3 cm.
10. The radius of the larger circle is 10 cm greater than the smaller circle, so it will be approximately:
r + 10 ≈ 18.3 + 10
r + 10 ≈ 28.3
11. Therefore, the radius of the larger circle is approximately 28.3 cm.
So, the radius of the smaller circle is approximately 18.3 cm, and the radius of the larger circle is approximately 28.3 cm.
complete question could be A piece of wire 136 cm long is cut into two pieces, and each piece is then bent into a circle. The radius of one of the two circles is 10 cm greater than the radius of the other. Find the radius (in cm) of the circles.